Now they show up: Department of Buildings officials at the scene of Thursday’s deadly building collapse in Morningside Heights.Tomas E. Gaston

How many more will die as a result of the city’s blind eye to building and construction accidents?

One week ago yesterday, in a column pointing out that, on a per-site basis, the Department of Health has 19 times more inspectors for restaurants than the Department of Buildings has for buildings, I wrote:

“What too often happens at sites nominally monitored by the DOB? Construction workers die in accidents on the job.”

On Thursday, one worker was killed and two more injured in a building collapse in Harlem.

Does the tragedy mean Mayor Bloomberg will reallocate resources from his restaurant-ruination squad to the Buildings Department, which is supposed to protect the public from real dangers, as opposed to “evidence of mouse droppings?”

Hah!

The DOH has one inspector for every 160 restaurants; the DOB, one inspector for every 3,075 buildings. (While not all the DOH squads are assigned to eateries full-time, DOB forces also have other duties — and some DOB inspectors focus only on specialized fields such as plumbing and electrical.)

To City Hall, the remote risk of salmonella infections — which fell by a mere 1 case per 70,000 New Yorkers since restaurant letter-grading began, the true meaning of what the DOH trumpeted as a 14 percent drop — takes precedence over the ongoing plague of building and sidewalk-bridge collapses, crane accidents and lethal elevator mishaps.

Buildings and construction disasters kill and injure real New Yorkers — compared with the unidentified, hypothetical ones who allegedly get upset stomachs in restaurants.

The DOB’s failure to rein in rogue landlords and contractors might be the result of City Hall’s not giving the agency the resources it needs; or to a longstanding, intermittent pattern of incompetence and corruption; or to a combination of the two. (Real-estate insiders say the DOB’s overall performance hassomewhat improved under Robert LiMandri, who became commissioner in 2008 after a series of interim bosses.)

But who’s more to blame hardly matters. Bottom line: The agency’s enforcement apparatus has no teeth, despite (rare) occasional work shutdowns that are typically imposed after someone’s been killed.

Anecdotal evidence isn’t definitive. Yet the city’s priorities seem reflected in the way it last fall banned the Algonquin Hotel’s famous cat from its lobby, where a succession of felines had freely roamed for 70 years.

The DOH said it was responding to a customer’s complaint that the cat was spotted in a “food-service area.”

Meanwhile, tenants at 243 W. 54th St. — a tiny, four-story apartment building sandwiched between mega-projects going up on either side — complained to the DOB for months of damage to their own building caused by demolition of 237 W. 54th next door.

The damage included a large hole in a foundation wall. Yet inspectors declined to cite the owners of the adjacent site for violations and, according to the tenants, at one point denied a hole even existed.

According to signs previously at the site, one contractor involved at 237 W. 54th was Breeze National — the same mob-linked outfit involved in Thursday’s tragedy in Harlem, where a wall collapse killed one man and injured two others. (Strangely, Breeze’s name doesn’t appear on the DOB Web site filings for the West 54th Street address.)

Now that demolition is over — mercifully without fatalities — residents of 243 W. 54th can look forward to a 34-story hotel going up against the side wall of their homes. There’s nothing wrong with that, of course — but is anyone at City Hall paying attention to safety?

With so much construction all over town, you’d think the need to protect the public would command the mayor’s urgent attention.

But given his strange priorities, don’t count on seeing the mouse-chasers deployed to the scenes of actual catastrophes any time soon.